Abstract

We demonstrate partial-transfer absorption imaging as a technique for repeatedly imaging an ultracold atomic ensemble with minimal perturbation. We prepare an atomic cloud in a state that is dark to the imaging light. We then use a microwave pulse to coherently transfer a small fraction of the ensemble to a bright state, which we image using in situ absorption imaging. The amplitude or duration of the microwave pulse controls the fractional transfer from the dark to the bright state. For small transfer fractions, we can image the atomic cloud up to 50 times before it is depleted. As a sample application, we repeatedly image an atomic cloud oscillating in a dipole trap to measure the trap frequency.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. M. Jasperse, “Faraday Magnetic Resonance Imaging of Bose-Einstein Condensates,” Ph.D. thesis, Monash University (2015).
  2. M. Andrews, M.-O. Mewes, N. van Druten, D. Durfee, D. Kurn, and W. Ketterle, “Direct, nondestructive observation of a Bose condensate,” Science 273(5271), 84–87 (1996).
    [Crossref]
  3. M. R. Andrews, C. G. Townsend, H. J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Observation of interference between two bose condensates,” Science 275(5300), 637–641 (1997).
    [Crossref]
  4. C. C. Bradley, C. A. Sackett, and R. G. Hulet, “Bose-Einstein Condensation of Lithium: Observation of Limited Condensate Number,” Phys. Rev. Lett. 78(6), 985–989 (1997).
    [Crossref]
  5. M. Gajdacz, P. L. Pedersen, T. Morch, A. J. Hilliard, J. Arlt, and J. F. Sherson, “Non-destructive Faraday imaging of dynamically controlled ultracold atoms,” Rev. Sci. Instrum. 84(8), 083105 (2013).
    [Crossref]
  6. F. Kaminski, N. S. Kampel, M. P. H. Steenstrup, A. Griesmaier, E. S. Polzik, and J. H. Müller, “In-situ dual-port polarization contrast imaging of Faraday rotation in a high optical depth ultracold 87Rb atomic ensemble,” Eur. Phys. J. D 66(9), 227 (2012).
    [Crossref]
  7. P. B. Wigley, P. J. Everitt, K. S. Hardman, M. R. Hush, C. H. Wei, M. A. Sooriyabandara, P. Manju, J. D. Close, N. P. Robins, and C. C. N. Kuhn, “Non-destructive shadowgraph imaging of ultra-cold atoms,” Opt. Lett. 41(20), 4795–4798 (2016).
    [Crossref]
  8. J. E. Lye, J. J. Hope, and J. D. Close, “Nondestructive dynamic detectors for Bose-Einstein condensates,” Phys. Rev. A 67(4), 043609 (2003).
    [Crossref]
  9. L. D. Turner, K. F. E. M. Domen, and R. E. Scholten, “Diffraction-contrast imaging of cold atoms,” Phys. Rev. A 72(3), 031403 (2005).
    [Crossref]
  10. D. V. Freilich, D. M. Bianchi, A. M. Kaufman, T. K. Langin, and D. S. Hall, “Real-Time Dynamics of Single Vortex Lines and Vortex Dipoles in a Bose-Einstein Condensate,” Science 329(5996), 1182–1185 (2010).
    [Crossref]
  11. A. Ramanathan, S. R. Muniz, K. C. Wright, R. P. Anderson, W. D. Phillips, K. Helmerson, and G. K. Campbell, “Partial-transfer absorption imaging: A versatile technique for optimal imaging of ultracold gases,” Rev. Sci. Instrum. 83(8), 083119 (2012).
    [Crossref]
  12. D. Genkina, L. M. Aycock, B. K. Stuhl, H.-I. Lu, R. A. Williams, and I. B. Spielman, “Feshbach enhanced s-wave scattering of fermions: direct observation with optimized absorption imaging,” New J. Phys. 18(1), 013001 (2015).
    [Crossref]
  13. G. Reinaudi, T. Lahaye, Z. Wang, and D. Guéry-Odelin, “Strong saturation absorption imaging of dense clouds of ultracold atoms,” Opt. Lett. 32(21), 3143–3145 (2007).
    [Crossref]
  14. The identification of commercial products is for information only and does not imply recommendation or endorsement by the National Institute of Standards and Technology.
  15. All uncertainties herein reflect the uncorrelated combination of single-sigma statistical and systematic uncertainties.
  16. J. C. Crocker and D. G. Grier, “Methods of Digital Video Microscopy for Colloidal Studies,” J. Colloid Interface Sci. 179(1), 298–310 (1996).
    [Crossref]

2016 (1)

2015 (1)

D. Genkina, L. M. Aycock, B. K. Stuhl, H.-I. Lu, R. A. Williams, and I. B. Spielman, “Feshbach enhanced s-wave scattering of fermions: direct observation with optimized absorption imaging,” New J. Phys. 18(1), 013001 (2015).
[Crossref]

2013 (1)

M. Gajdacz, P. L. Pedersen, T. Morch, A. J. Hilliard, J. Arlt, and J. F. Sherson, “Non-destructive Faraday imaging of dynamically controlled ultracold atoms,” Rev. Sci. Instrum. 84(8), 083105 (2013).
[Crossref]

2012 (2)

F. Kaminski, N. S. Kampel, M. P. H. Steenstrup, A. Griesmaier, E. S. Polzik, and J. H. Müller, “In-situ dual-port polarization contrast imaging of Faraday rotation in a high optical depth ultracold 87Rb atomic ensemble,” Eur. Phys. J. D 66(9), 227 (2012).
[Crossref]

A. Ramanathan, S. R. Muniz, K. C. Wright, R. P. Anderson, W. D. Phillips, K. Helmerson, and G. K. Campbell, “Partial-transfer absorption imaging: A versatile technique for optimal imaging of ultracold gases,” Rev. Sci. Instrum. 83(8), 083119 (2012).
[Crossref]

2010 (1)

D. V. Freilich, D. M. Bianchi, A. M. Kaufman, T. K. Langin, and D. S. Hall, “Real-Time Dynamics of Single Vortex Lines and Vortex Dipoles in a Bose-Einstein Condensate,” Science 329(5996), 1182–1185 (2010).
[Crossref]

2007 (1)

2005 (1)

L. D. Turner, K. F. E. M. Domen, and R. E. Scholten, “Diffraction-contrast imaging of cold atoms,” Phys. Rev. A 72(3), 031403 (2005).
[Crossref]

2003 (1)

J. E. Lye, J. J. Hope, and J. D. Close, “Nondestructive dynamic detectors for Bose-Einstein condensates,” Phys. Rev. A 67(4), 043609 (2003).
[Crossref]

1997 (2)

M. R. Andrews, C. G. Townsend, H. J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Observation of interference between two bose condensates,” Science 275(5300), 637–641 (1997).
[Crossref]

C. C. Bradley, C. A. Sackett, and R. G. Hulet, “Bose-Einstein Condensation of Lithium: Observation of Limited Condensate Number,” Phys. Rev. Lett. 78(6), 985–989 (1997).
[Crossref]

1996 (2)

M. Andrews, M.-O. Mewes, N. van Druten, D. Durfee, D. Kurn, and W. Ketterle, “Direct, nondestructive observation of a Bose condensate,” Science 273(5271), 84–87 (1996).
[Crossref]

J. C. Crocker and D. G. Grier, “Methods of Digital Video Microscopy for Colloidal Studies,” J. Colloid Interface Sci. 179(1), 298–310 (1996).
[Crossref]

Anderson, R. P.

A. Ramanathan, S. R. Muniz, K. C. Wright, R. P. Anderson, W. D. Phillips, K. Helmerson, and G. K. Campbell, “Partial-transfer absorption imaging: A versatile technique for optimal imaging of ultracold gases,” Rev. Sci. Instrum. 83(8), 083119 (2012).
[Crossref]

Andrews, M.

M. Andrews, M.-O. Mewes, N. van Druten, D. Durfee, D. Kurn, and W. Ketterle, “Direct, nondestructive observation of a Bose condensate,” Science 273(5271), 84–87 (1996).
[Crossref]

Andrews, M. R.

M. R. Andrews, C. G. Townsend, H. J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Observation of interference between two bose condensates,” Science 275(5300), 637–641 (1997).
[Crossref]

Arlt, J.

M. Gajdacz, P. L. Pedersen, T. Morch, A. J. Hilliard, J. Arlt, and J. F. Sherson, “Non-destructive Faraday imaging of dynamically controlled ultracold atoms,” Rev. Sci. Instrum. 84(8), 083105 (2013).
[Crossref]

Aycock, L. M.

D. Genkina, L. M. Aycock, B. K. Stuhl, H.-I. Lu, R. A. Williams, and I. B. Spielman, “Feshbach enhanced s-wave scattering of fermions: direct observation with optimized absorption imaging,” New J. Phys. 18(1), 013001 (2015).
[Crossref]

Bianchi, D. M.

D. V. Freilich, D. M. Bianchi, A. M. Kaufman, T. K. Langin, and D. S. Hall, “Real-Time Dynamics of Single Vortex Lines and Vortex Dipoles in a Bose-Einstein Condensate,” Science 329(5996), 1182–1185 (2010).
[Crossref]

Bradley, C. C.

C. C. Bradley, C. A. Sackett, and R. G. Hulet, “Bose-Einstein Condensation of Lithium: Observation of Limited Condensate Number,” Phys. Rev. Lett. 78(6), 985–989 (1997).
[Crossref]

Campbell, G. K.

A. Ramanathan, S. R. Muniz, K. C. Wright, R. P. Anderson, W. D. Phillips, K. Helmerson, and G. K. Campbell, “Partial-transfer absorption imaging: A versatile technique for optimal imaging of ultracold gases,” Rev. Sci. Instrum. 83(8), 083119 (2012).
[Crossref]

Close, J. D.

Crocker, J. C.

J. C. Crocker and D. G. Grier, “Methods of Digital Video Microscopy for Colloidal Studies,” J. Colloid Interface Sci. 179(1), 298–310 (1996).
[Crossref]

Durfee, D.

M. Andrews, M.-O. Mewes, N. van Druten, D. Durfee, D. Kurn, and W. Ketterle, “Direct, nondestructive observation of a Bose condensate,” Science 273(5271), 84–87 (1996).
[Crossref]

Durfee, D. S.

M. R. Andrews, C. G. Townsend, H. J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Observation of interference between two bose condensates,” Science 275(5300), 637–641 (1997).
[Crossref]

Everitt, P. J.

Freilich, D. V.

D. V. Freilich, D. M. Bianchi, A. M. Kaufman, T. K. Langin, and D. S. Hall, “Real-Time Dynamics of Single Vortex Lines and Vortex Dipoles in a Bose-Einstein Condensate,” Science 329(5996), 1182–1185 (2010).
[Crossref]

Gajdacz, M.

M. Gajdacz, P. L. Pedersen, T. Morch, A. J. Hilliard, J. Arlt, and J. F. Sherson, “Non-destructive Faraday imaging of dynamically controlled ultracold atoms,” Rev. Sci. Instrum. 84(8), 083105 (2013).
[Crossref]

Genkina, D.

D. Genkina, L. M. Aycock, B. K. Stuhl, H.-I. Lu, R. A. Williams, and I. B. Spielman, “Feshbach enhanced s-wave scattering of fermions: direct observation with optimized absorption imaging,” New J. Phys. 18(1), 013001 (2015).
[Crossref]

Grier, D. G.

J. C. Crocker and D. G. Grier, “Methods of Digital Video Microscopy for Colloidal Studies,” J. Colloid Interface Sci. 179(1), 298–310 (1996).
[Crossref]

Griesmaier, A.

F. Kaminski, N. S. Kampel, M. P. H. Steenstrup, A. Griesmaier, E. S. Polzik, and J. H. Müller, “In-situ dual-port polarization contrast imaging of Faraday rotation in a high optical depth ultracold 87Rb atomic ensemble,” Eur. Phys. J. D 66(9), 227 (2012).
[Crossref]

Guéry-Odelin, D.

Hall, D. S.

D. V. Freilich, D. M. Bianchi, A. M. Kaufman, T. K. Langin, and D. S. Hall, “Real-Time Dynamics of Single Vortex Lines and Vortex Dipoles in a Bose-Einstein Condensate,” Science 329(5996), 1182–1185 (2010).
[Crossref]

Hardman, K. S.

Helmerson, K.

A. Ramanathan, S. R. Muniz, K. C. Wright, R. P. Anderson, W. D. Phillips, K. Helmerson, and G. K. Campbell, “Partial-transfer absorption imaging: A versatile technique for optimal imaging of ultracold gases,” Rev. Sci. Instrum. 83(8), 083119 (2012).
[Crossref]

Hilliard, A. J.

M. Gajdacz, P. L. Pedersen, T. Morch, A. J. Hilliard, J. Arlt, and J. F. Sherson, “Non-destructive Faraday imaging of dynamically controlled ultracold atoms,” Rev. Sci. Instrum. 84(8), 083105 (2013).
[Crossref]

Hope, J. J.

J. E. Lye, J. J. Hope, and J. D. Close, “Nondestructive dynamic detectors for Bose-Einstein condensates,” Phys. Rev. A 67(4), 043609 (2003).
[Crossref]

Hulet, R. G.

C. C. Bradley, C. A. Sackett, and R. G. Hulet, “Bose-Einstein Condensation of Lithium: Observation of Limited Condensate Number,” Phys. Rev. Lett. 78(6), 985–989 (1997).
[Crossref]

Hush, M. R.

Jasperse, M.

M. Jasperse, “Faraday Magnetic Resonance Imaging of Bose-Einstein Condensates,” Ph.D. thesis, Monash University (2015).

Kaminski, F.

F. Kaminski, N. S. Kampel, M. P. H. Steenstrup, A. Griesmaier, E. S. Polzik, and J. H. Müller, “In-situ dual-port polarization contrast imaging of Faraday rotation in a high optical depth ultracold 87Rb atomic ensemble,” Eur. Phys. J. D 66(9), 227 (2012).
[Crossref]

Kampel, N. S.

F. Kaminski, N. S. Kampel, M. P. H. Steenstrup, A. Griesmaier, E. S. Polzik, and J. H. Müller, “In-situ dual-port polarization contrast imaging of Faraday rotation in a high optical depth ultracold 87Rb atomic ensemble,” Eur. Phys. J. D 66(9), 227 (2012).
[Crossref]

Kaufman, A. M.

D. V. Freilich, D. M. Bianchi, A. M. Kaufman, T. K. Langin, and D. S. Hall, “Real-Time Dynamics of Single Vortex Lines and Vortex Dipoles in a Bose-Einstein Condensate,” Science 329(5996), 1182–1185 (2010).
[Crossref]

Ketterle, W.

M. R. Andrews, C. G. Townsend, H. J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Observation of interference between two bose condensates,” Science 275(5300), 637–641 (1997).
[Crossref]

M. Andrews, M.-O. Mewes, N. van Druten, D. Durfee, D. Kurn, and W. Ketterle, “Direct, nondestructive observation of a Bose condensate,” Science 273(5271), 84–87 (1996).
[Crossref]

Kuhn, C. C. N.

Kurn, D.

M. Andrews, M.-O. Mewes, N. van Druten, D. Durfee, D. Kurn, and W. Ketterle, “Direct, nondestructive observation of a Bose condensate,” Science 273(5271), 84–87 (1996).
[Crossref]

Kurn, D. M.

M. R. Andrews, C. G. Townsend, H. J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Observation of interference between two bose condensates,” Science 275(5300), 637–641 (1997).
[Crossref]

Lahaye, T.

Langin, T. K.

D. V. Freilich, D. M. Bianchi, A. M. Kaufman, T. K. Langin, and D. S. Hall, “Real-Time Dynamics of Single Vortex Lines and Vortex Dipoles in a Bose-Einstein Condensate,” Science 329(5996), 1182–1185 (2010).
[Crossref]

Lu, H.-I.

D. Genkina, L. M. Aycock, B. K. Stuhl, H.-I. Lu, R. A. Williams, and I. B. Spielman, “Feshbach enhanced s-wave scattering of fermions: direct observation with optimized absorption imaging,” New J. Phys. 18(1), 013001 (2015).
[Crossref]

Lye, J. E.

J. E. Lye, J. J. Hope, and J. D. Close, “Nondestructive dynamic detectors for Bose-Einstein condensates,” Phys. Rev. A 67(4), 043609 (2003).
[Crossref]

M. Domen, K. F. E.

L. D. Turner, K. F. E. M. Domen, and R. E. Scholten, “Diffraction-contrast imaging of cold atoms,” Phys. Rev. A 72(3), 031403 (2005).
[Crossref]

Manju, P.

Mewes, M.-O.

M. Andrews, M.-O. Mewes, N. van Druten, D. Durfee, D. Kurn, and W. Ketterle, “Direct, nondestructive observation of a Bose condensate,” Science 273(5271), 84–87 (1996).
[Crossref]

Miesner, H. J.

M. R. Andrews, C. G. Townsend, H. J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Observation of interference between two bose condensates,” Science 275(5300), 637–641 (1997).
[Crossref]

Morch, T.

M. Gajdacz, P. L. Pedersen, T. Morch, A. J. Hilliard, J. Arlt, and J. F. Sherson, “Non-destructive Faraday imaging of dynamically controlled ultracold atoms,” Rev. Sci. Instrum. 84(8), 083105 (2013).
[Crossref]

Müller, J. H.

F. Kaminski, N. S. Kampel, M. P. H. Steenstrup, A. Griesmaier, E. S. Polzik, and J. H. Müller, “In-situ dual-port polarization contrast imaging of Faraday rotation in a high optical depth ultracold 87Rb atomic ensemble,” Eur. Phys. J. D 66(9), 227 (2012).
[Crossref]

Muniz, S. R.

A. Ramanathan, S. R. Muniz, K. C. Wright, R. P. Anderson, W. D. Phillips, K. Helmerson, and G. K. Campbell, “Partial-transfer absorption imaging: A versatile technique for optimal imaging of ultracold gases,” Rev. Sci. Instrum. 83(8), 083119 (2012).
[Crossref]

Pedersen, P. L.

M. Gajdacz, P. L. Pedersen, T. Morch, A. J. Hilliard, J. Arlt, and J. F. Sherson, “Non-destructive Faraday imaging of dynamically controlled ultracold atoms,” Rev. Sci. Instrum. 84(8), 083105 (2013).
[Crossref]

Phillips, W. D.

A. Ramanathan, S. R. Muniz, K. C. Wright, R. P. Anderson, W. D. Phillips, K. Helmerson, and G. K. Campbell, “Partial-transfer absorption imaging: A versatile technique for optimal imaging of ultracold gases,” Rev. Sci. Instrum. 83(8), 083119 (2012).
[Crossref]

Polzik, E. S.

F. Kaminski, N. S. Kampel, M. P. H. Steenstrup, A. Griesmaier, E. S. Polzik, and J. H. Müller, “In-situ dual-port polarization contrast imaging of Faraday rotation in a high optical depth ultracold 87Rb atomic ensemble,” Eur. Phys. J. D 66(9), 227 (2012).
[Crossref]

Ramanathan, A.

A. Ramanathan, S. R. Muniz, K. C. Wright, R. P. Anderson, W. D. Phillips, K. Helmerson, and G. K. Campbell, “Partial-transfer absorption imaging: A versatile technique for optimal imaging of ultracold gases,” Rev. Sci. Instrum. 83(8), 083119 (2012).
[Crossref]

Reinaudi, G.

Robins, N. P.

Sackett, C. A.

C. C. Bradley, C. A. Sackett, and R. G. Hulet, “Bose-Einstein Condensation of Lithium: Observation of Limited Condensate Number,” Phys. Rev. Lett. 78(6), 985–989 (1997).
[Crossref]

Scholten, R. E.

L. D. Turner, K. F. E. M. Domen, and R. E. Scholten, “Diffraction-contrast imaging of cold atoms,” Phys. Rev. A 72(3), 031403 (2005).
[Crossref]

Sherson, J. F.

M. Gajdacz, P. L. Pedersen, T. Morch, A. J. Hilliard, J. Arlt, and J. F. Sherson, “Non-destructive Faraday imaging of dynamically controlled ultracold atoms,” Rev. Sci. Instrum. 84(8), 083105 (2013).
[Crossref]

Sooriyabandara, M. A.

Spielman, I. B.

D. Genkina, L. M. Aycock, B. K. Stuhl, H.-I. Lu, R. A. Williams, and I. B. Spielman, “Feshbach enhanced s-wave scattering of fermions: direct observation with optimized absorption imaging,” New J. Phys. 18(1), 013001 (2015).
[Crossref]

Steenstrup, M. P. H.

F. Kaminski, N. S. Kampel, M. P. H. Steenstrup, A. Griesmaier, E. S. Polzik, and J. H. Müller, “In-situ dual-port polarization contrast imaging of Faraday rotation in a high optical depth ultracold 87Rb atomic ensemble,” Eur. Phys. J. D 66(9), 227 (2012).
[Crossref]

Stuhl, B. K.

D. Genkina, L. M. Aycock, B. K. Stuhl, H.-I. Lu, R. A. Williams, and I. B. Spielman, “Feshbach enhanced s-wave scattering of fermions: direct observation with optimized absorption imaging,” New J. Phys. 18(1), 013001 (2015).
[Crossref]

Townsend, C. G.

M. R. Andrews, C. G. Townsend, H. J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Observation of interference between two bose condensates,” Science 275(5300), 637–641 (1997).
[Crossref]

Turner, L. D.

L. D. Turner, K. F. E. M. Domen, and R. E. Scholten, “Diffraction-contrast imaging of cold atoms,” Phys. Rev. A 72(3), 031403 (2005).
[Crossref]

van Druten, N.

M. Andrews, M.-O. Mewes, N. van Druten, D. Durfee, D. Kurn, and W. Ketterle, “Direct, nondestructive observation of a Bose condensate,” Science 273(5271), 84–87 (1996).
[Crossref]

Wang, Z.

Wei, C. H.

Wigley, P. B.

Williams, R. A.

D. Genkina, L. M. Aycock, B. K. Stuhl, H.-I. Lu, R. A. Williams, and I. B. Spielman, “Feshbach enhanced s-wave scattering of fermions: direct observation with optimized absorption imaging,” New J. Phys. 18(1), 013001 (2015).
[Crossref]

Wright, K. C.

A. Ramanathan, S. R. Muniz, K. C. Wright, R. P. Anderson, W. D. Phillips, K. Helmerson, and G. K. Campbell, “Partial-transfer absorption imaging: A versatile technique for optimal imaging of ultracold gases,” Rev. Sci. Instrum. 83(8), 083119 (2012).
[Crossref]

Eur. Phys. J. D (1)

F. Kaminski, N. S. Kampel, M. P. H. Steenstrup, A. Griesmaier, E. S. Polzik, and J. H. Müller, “In-situ dual-port polarization contrast imaging of Faraday rotation in a high optical depth ultracold 87Rb atomic ensemble,” Eur. Phys. J. D 66(9), 227 (2012).
[Crossref]

J. Colloid Interface Sci. (1)

J. C. Crocker and D. G. Grier, “Methods of Digital Video Microscopy for Colloidal Studies,” J. Colloid Interface Sci. 179(1), 298–310 (1996).
[Crossref]

New J. Phys. (1)

D. Genkina, L. M. Aycock, B. K. Stuhl, H.-I. Lu, R. A. Williams, and I. B. Spielman, “Feshbach enhanced s-wave scattering of fermions: direct observation with optimized absorption imaging,” New J. Phys. 18(1), 013001 (2015).
[Crossref]

Opt. Lett. (2)

Phys. Rev. A (2)

J. E. Lye, J. J. Hope, and J. D. Close, “Nondestructive dynamic detectors for Bose-Einstein condensates,” Phys. Rev. A 67(4), 043609 (2003).
[Crossref]

L. D. Turner, K. F. E. M. Domen, and R. E. Scholten, “Diffraction-contrast imaging of cold atoms,” Phys. Rev. A 72(3), 031403 (2005).
[Crossref]

Phys. Rev. Lett. (1)

C. C. Bradley, C. A. Sackett, and R. G. Hulet, “Bose-Einstein Condensation of Lithium: Observation of Limited Condensate Number,” Phys. Rev. Lett. 78(6), 985–989 (1997).
[Crossref]

Rev. Sci. Instrum. (2)

M. Gajdacz, P. L. Pedersen, T. Morch, A. J. Hilliard, J. Arlt, and J. F. Sherson, “Non-destructive Faraday imaging of dynamically controlled ultracold atoms,” Rev. Sci. Instrum. 84(8), 083105 (2013).
[Crossref]

A. Ramanathan, S. R. Muniz, K. C. Wright, R. P. Anderson, W. D. Phillips, K. Helmerson, and G. K. Campbell, “Partial-transfer absorption imaging: A versatile technique for optimal imaging of ultracold gases,” Rev. Sci. Instrum. 83(8), 083119 (2012).
[Crossref]

Science (3)

M. Andrews, M.-O. Mewes, N. van Druten, D. Durfee, D. Kurn, and W. Ketterle, “Direct, nondestructive observation of a Bose condensate,” Science 273(5271), 84–87 (1996).
[Crossref]

M. R. Andrews, C. G. Townsend, H. J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Observation of interference between two bose condensates,” Science 275(5300), 637–641 (1997).
[Crossref]

D. V. Freilich, D. M. Bianchi, A. M. Kaufman, T. K. Langin, and D. S. Hall, “Real-Time Dynamics of Single Vortex Lines and Vortex Dipoles in a Bose-Einstein Condensate,” Science 329(5996), 1182–1185 (2010).
[Crossref]

Other (3)

M. Jasperse, “Faraday Magnetic Resonance Imaging of Bose-Einstein Condensates,” Ph.D. thesis, Monash University (2015).

The identification of commercial products is for information only and does not imply recommendation or endorsement by the National Institute of Standards and Technology.

All uncertainties herein reflect the uncorrelated combination of single-sigma statistical and systematic uncertainties.

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Figures (8)

Fig. 1.
Fig. 1. (a) Level diagram for the partial-transfer absorption imaging technique. The atoms are prepared in the dark state $|d\rangle$, and a fraction of the atoms are transferred from $|d\rangle$ to $|b\rangle$ by a coherent pulse (green) of frequency $\Omega _{bd}$. (b) A simple schematic of the partial-transfer absorption imaging system. The pink lines depict the probe beam, and the dotted region indicates a small solid angle of the light of frequency $\Omega _{be}$, emitted isotropically from the cloud as the atoms decay from $|e\rangle$ to $|b\rangle$. The light is collected by the imaging lenses and re-focused onto a charge-coupled device (CCD).
Fig. 2.
Fig. 2. Partial-transfer absorption imaging. (a) We used the hyperfine structure of the $5^{2}S_{1/2}$ electronic ground state of $^{87}$Rb to resolve the $|d\rangle$ and $|b\rangle$ states, and we imaged on the D$_{2}$ transition. A 6.8 GHz coherent microwave pulse (green) coupled the dark state, $|1,-1\rangle$, to the bright state, $|2,-2\rangle$. A $\lambda =$ 780 nm laser (pink) coupled the bright state to the excited state, $|3,-3\rangle$. (b) The imaging system, including the TOF and in situ imaging paths, is shown. $L_{1}$ is a compound lens pair consisting of a 60 mm achromatic doublet lens and a 300 mm plano-convex singlet lens. $L_{2}$ is a second compound lens pair consisting of a 500 mm plano-convex singlet and a 250 mm achromatic lens. $L_{3}$ is a 150 mm achromatic doublet. $L_{4}$ is a 750 mm achromatic doublet. (c) Six PTAI images taken of the same BEC using the in situ CCD camera as shown. For each image, a 12 µs pulse at a Rabi frequency of approximately 14.3 kHz transferred a fraction of the cloud from the dark state to the bright state. The atoms were imaged on the cycling transition.
Fig. 3.
Fig. 3. Coherent transfer measured using TOF and in situ absorption imaging. (a) The fraction of atoms transferred into $|F=2\rangle$ after variable microwave pulse duration shows Rabi oscillation with a frequency $\Omega _{\mathrm {bd}}/2\pi = 5.03(33)$ kHz. We measured the transfer fraction using TOF absorption imaging (blue squares) and in situ absorption imaging (black circles). The grey shading indicates regions where the optical depth of a typical shot is $\gtrapprox$ 3. The transfer fraction in the grey regions is underrepresented due to extinction of the probe beam in high-OD atomic clouds. Atom number uncertainties are smaller than the data points. (b) The measured fraction transferred into the bright state increases with the microwave pulse amplitude. As $\epsilon$ is increased by strengthening the pulse, the number of atoms $N_{b}^{(1)}$ in the first PTAI shot increases linearly for $\epsilon \leq$ 0.04. Error bars represent the 95% confidence bounds on $N_{b}^{(1)}$.
Fig. 4.
Fig. 4. The effect of transfer strength on measured atom number in a PTAI series. (a) Examples of weak transfer (top image) and strong transfer (second image) are shown, each displaying the first 15 images of the PTAI series. The second pair of images represent the integrated atom number in each of the 15 images for the weak transfer and strong transfer examples above. (b) Measured atom number varies with transfer strength, here determined by the microwave pulse duration. Each row represents the total atom number measured in each of 58 images of a single BEC, taken 4 ms apart, in chronological order from left to right, for a given pulse duration. The Rabi frequency was about 4.9 kHz. (c) The integrated atom number is plotted as a function of shot index for both the weak transfer series (triangles) and the strong transfer series (squares). To determine $N_{b}^{(1)}$ and $\xi$ for a given transfer fraction, the data is fit to the exponential in Eq. (5) (red) and the rescattering model based on Eq. (9) (blue).
Fig. 5.
Fig. 5. The tuneability of $\xi$. The red curves depict the expected values of $\xi$ based on the model in Section 1. The black circles depict the value of $\xi$ obtained from an exponential fit as shown in Fig. 4(b), and the blue squares depict the values of $\xi$ obtained from a fit to a model which accounts for atomic recoil after coherent transfer, as described in Eq. (9), with $\beta = 0.91$. Error bars represent 95% confidence intervals. (a) The longevity $\xi$ varies as a function of the duration of the microwave pulse. (b) The longevity $\xi$ varies as a function of the fraction transferred. Here the longevity is tuned by varying the amplitude of the microwave pulse.
Fig. 6.
Fig. 6. Single pixel signal-to-noise ratio of multi-shot PTAI images. (a) The SNR was measured as described in Eq. (4.). Because the microwave pulse duration was used to vary $\epsilon$, which is defined according to Eq. (3), the vertical axis increases non-linearly from 0 to 1. (b) The SNR was modeled based on the image OD and the background noise. (c) For $\epsilon = 0.02$, the SNR of the earliest shots is about 4 and remains near 2 even after 20 shots. The red curve represents the modeled SNR. (d) For $\epsilon = 0.50$, the SNR of the first shots is in excess of 4 but drops below 2 in less than 10 shots. The red curve represents the modeled SNR.
Fig. 7.
Fig. 7. A collective dipole excitation in a BEC. A series of spatially low-passed images of the same BEC are inset at the top of the figure, showing a dipole mode. For ease of viewing, only the first and last 9 PTAI shots are shown. The center of mass position of the BEC along $\mathbf {e}_{x}$ is plotted as a function of PTAI shot number. The data show a clear oscillation without damping.
Fig. 8.
Fig. 8. (a) The series of curves each shows $n \sigma _{0}$ as a function of $I/I_{\mathrm {sat}}$ for a candidate value of $\alpha$ along with a linear fit. (b) Here the slope of the linear fit to each $n \sigma _{0} (\alpha )$ curve is shown as a function of the candidate value of $\alpha$. The value chosen for $\alpha$ is where the slope goes to zero.

Equations (11)

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d I ~ d z = n σ 0 α I ~ ( z ) 1 + I ~ ,
σ 0 n 2 D = α l n ( I ~ f I ~ i ) + I ~ i I ~ f ,
ϵ = s i n 2 ( Ω b d t 2 ) .
N b ( m ) = ϵ N d ( 1 ) ( 1 ϵ ) m 1 = N b ( 1 ) c o s 2 ( m 1 ) ( Ω b d t 2 ) ,
N b ( m ) = N b ( 1 ) exp ( m 1 ξ ) , w i t h ξ = 1 / l n ( 1 ϵ )
t 2 π ( q + 1 2 ) / Ω b d ,
d n s c a t t d t = [ ( 1 ϵ ) n n s c a t t ] σ v [ ϵ n + n s c a t t ]
ϵ eff = 1 + 1 1 + e n t v σ ϵ 1 + ϵ
N d ( m + 1 ) = N d ( m ) 1 ϵ 1 + ϵ ( e N d ( m ) β 1 ) ,
S N R = μ s / σ s
S N R m o d e l = OD Δ 0 ( 2 1 + e OD ) 1 / 2 ,